## Abstract

To define the spectral domain of the Newton volume integral, the kernel of Newton’s integral, i.e., the reciprocal value of the spatial distance is expanded into a series of the Legendre polynomials. It can be done only if the condition of convergence is satisfied (Hobson 1931; Sternberg and Smith, 1952), so that the ratio of the geocentric radii of the computation and integration points has to be ≤ 1. Considering for the gravitational field generated by atmosphere and topography, the spectral domain of Newton’s volume integral is discussed. Based on a theoretical investigation the analytical formulae for the gravitational potential and attraction are then introduced.

Translated title of the contribution | Spectral domain of newton’s integral |
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Original language | Italian |

Pages (from-to) | 61-73 |

Number of pages | 13 |

Journal | Bollettino di Geodesia e Scienze Affini |

Volume | 64 |

Issue number | 2 |

Publication status | Published - 2005 |

Externally published | Yes |

## Keywords

- Atmosphere
- Gravity
- Legendre polynomials
- Newton’s integral
- Topography

## ASJC Scopus subject areas

- Engineering(all)